Peridynamics and Extended Finite Element Method-Based Techniques for Mixed-Mode Crack Propagation in Brittle Materials

In solid mechanics, material defects and imperfections significantly influence the overall mechanical behaviour of structures, despite their localised nature. This work investigates Mode I, Mode II and Mixed-mode crack propagation using two different approaches: linear elastic fracture mechanics (LEFM) and bond-based peridynamics (PD). For LEFM, crack path progression is simulated using the Extended Finite Element Method (XFEM), which avoids the need for a mesh conforming to the crack geometry by locally enriching the nodes within the influence domain of discontinuities and singularities. For PD, a classical continuum mechanics-peridynamics (CCM-PD) coupling strategy is employed, combining the capability of PD to handle displacement field discontinuities with the computational efficiency of CCM-based modelling approaches, such as those based on the Finite Element Method (FEM). All formulations are developed within a 2D linearised framework and implemented through in-house codes. The correspondence between LEFM-based XFEM and CCM-PD coupled models is analysed through benchmark problems: a finite plate with an edge crack under uniform tension for Mode I crack propagation, a finite plate with an edge crack under both uniform tension and shear for Mixed-mode crack propagation and to investigate the effect of varying mode-mixity ratio on crack path, and a finite plate with an edge crack under uniform shear for Mode II crack propagation. The study concludes by comparing the results of the two approaches and suggests directions for future developments.